Kinetic Energy of Hemi-sphere: The Energy Method

  • Thread starter Thread starter robip
  • Start date Start date
  • Tags Tags
    Energy Method
AI Thread Summary
To determine the kinetic energy of a solid hemisphere during small amplitude rocking motion, it is essential to analyze how the center of mass (CM) is affected by tilting. The energy involved in the motion is derived from the elevation change of the CM as the hemisphere rocks. The CM is located along the axis of symmetry, approximately at 3/8 of the radius from the flat surface. The discussion highlights the challenge of applying the energy method to this scenario, with participants seeking guidance on formulating the kinetic energy expression. Understanding the relationship between the CM's height change and the resulting kinetic energy is crucial for solving the problem.
robip
Messages
11
Reaction score
0

Homework Statement


A solid hemi-sphere of radius r rests on a hard flat surface. If rolled slightly in 1 direction and released, the hemisphere will rock from side to side, assume no slipping. Write an expression for the kinetic energy of the hemi-sphere during the small amplitude motion


Homework Equations



0.5mv^2

The Attempt at a Solution



Not sure even where to start :cry:
 
Physics news on Phys.org
Start by figuring out how the center of mass of the hemisphere is raised when it is tilted to some angle theta. That raising of the CM is what provides the energy to make the motion happen.
 
thanks I will give it a go and get back, I am assuming that the center of mass would be through the axii of symetry and 3/8th's the radius i.e x0,y0,z3r/8
 
ok i am completely stuck, i have no idea how to work this out
 
Can you do it for a traditional pendulum?
 

Similar threads

Kinetic Energy of a Cylinder Rolling Without Slipping
Replies
21
Views
4K
I I'm calculating more energy out than I put in
3
Replies
138
Views
7K
Which sphere reaches the bottom of the inclined plane first
Replies
19
Views
4K
I Is Mechanical Energy Conservation Free of Ambiguity - follow up
2
Replies
77
Views
4K
The length of a pendulum that is equivalent to a rocking hemisphere
Replies
5
Views
2K
Conservation of energy problem: Ball rolling down inclined plane and then through a loop-the-loop
Replies
10
Views
2K
Kinetic energy of solid sphere that is rolling
Replies
2
Views
6K
Kinetic and potential energy of a particle attracted by charged sphere
Replies
6
Views
1K
Conservation of Energy with Gravitational Potential Energy
Replies
6
Views
2K
Acceleration of a uniform solid sphere rolling down incline
Replies
1
Views
3K

Hot Threads

Recent Insights

Back
Top